Combining Texts

All the ideas for 'Laches', 'Russell's Mathematical Logic' and 'Tarski on Truth and Logical Consequence'

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13 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
291 Don't assume that wisdom is the automatic consequence of old age [Plato]
2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
19323 'Snow is white' depends on meaning; whether snow is white depends on snow [Etchemendy]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
19137 We can get a substantive account of Tarski's truth by adding primitive 'true' to the object language [Etchemendy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21716 In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042 Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046 The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10043 Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
293 Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]